Diagonal reduction algebra and reflection equation

TL;DR

This paper explores the diagonal reduction algebra of gl(n) using R-matrix formalism, introducing central elements and a braided bialgebra structure, advancing the algebraic understanding of these structures.

Contribution

It provides a new R-matrix based description of D(gl(n)), including central elements and a braided bialgebra framework, which were not previously detailed.

Findings

Presented two families of central elements.

Described the braided bialgebra structure of D(gl(n)).

Connected the algebra to R-matrix formalism.

Abstract

We describe the diagonal reduction algebra D(gl(n)) of the Lie algebra gl(n) in the R-matrix formalism. As a byproduct we present two families of central elements and the braided bialgebra structure of D(gl(n)).